Such a technique is known in relation to an exhaust gas purification system having a particulate filter arranged in an exhaust passage of an internal combustion engine that the PM (Particulate Matter) accumulation amount and the ash accumulation amount of the particulate filter are calculated on the basis of, for example, the operation history of the internal combustion engine, and a filter regeneration process is executed in order to oxidize and remove PM collected by the particulate filter if the PM accumulation amount arrives at a certain threshold value (see, for example, Patent Literature 1).